Question

How many distinct sets of three positive integers have a mean of 6, a median of 7. and no mode?​

Answer 1

Answer:

there are 4 sets.

Step-by-step explanation:

Let A , B , C are the sets of positive integers

Now n is 3 which is odd

Therefore as given Median is 7

In A, B, C ;   B is median

Therefore B = 7

Now mean = 6

Possible combination of A+C= 11 is

A=1 C= 10

A= 2 C= 9

A= 3 C= 8

A= 4 C= 7

A= 5 C= 6

Now the function have no mode

therefore we exclude A= 4 and C= 7

The distinct sets are 1) 1, 7, 10 ;2) 2 , 7, 9 ; 3) 3, 7, 8 ; 4) 5, 7, 6

Hence, there are distinct 4 sets of three positive integers that have mean of 6 median 7 and no mode